Chapter 13.5, Problem 14ST1

a.

To determine

To fill: in the blank

Answer to Problem 14ST1

The answer is $\left(-3,2\right)+\left(7,-11\right)=\underset{\_}{4,-9}$

Explanation of Solution

Given information: $\left(-3,2\right)+\left(7,-11\right)=\underset{\_}{}$

Vectors can be added by the following simple rule

  $\begin{array}{l}\left(a,b\right)+\left(c,d\right)=a+c,b+d\\ \left(-3,2\right)+\left(7,-11\right)=-3+7,2+\left(-11\right)\\ \left(-3,2\right)+\left(7,-11\right)=4,-9\end{array}$

b.

To determine

To fill: in the blank

Answer to Problem 14ST1

The answer is $3\left(4,-1\right)+\left(-2\right)\left(-5,3\right)=\underset{\_}{22,-9}$

Explanation of Solution

Given information: $3\left(4,-1\right)+\left(-2\right)\left(-5,3\right)=\underset{\_}{}$

Vectors can be added by the following simple rule

  $\begin{array}{l}\left(a,b\right)+\left(c,d\right)=a+c,b+d\\ 3\left(4,-1\right)+\left(-2\right)\left(-5,3\right)=\left(12,3\right)+\left(10,-6\right)\\ 3\left(4,-1\right)+\left(-2\right)\left(-5,3\right)=12+10,3+\left(-6\right)\\ 3\left(4,-1\right)+\left(-2\right)\left(-5,3\right)=22,-9\end{array}$